I. Field
The present invention relates generally to communication, and more specifically to techniques for decomposing matrices.
II. Background
A multiple-input multiple-output (MIMO) communication system employs multiple (T) transmit antennas at a transmitting station and multiple (R) receive antennas at a receiving station for data transmission. A MIMO channel formed by the T transmit antennas and the R receive antennas may be decomposed into S spatial channels, where S≦min {T, R}. The S spatial channels may be used to transmit data in a manner to achieve higher overall throughput and/or greater reliability.
A MIMO channel response may be characterized by an R×T channel response matrix H, which contains complex channel gains for all of the different pairs of transmit and receive antennas. The channel response matrix H may be diagonalized to obtain S eigenmodes, which may be viewed as orthogonal spatial channels of the MIMO channel. Improved performance may be achieved by transmitting data on the eigenmodes of the MIMO channel.
The channel response matrix H may be diagonalized by performing either singular value decomposition of H or eigenvalue decomposition of a correlation matrix of H. The singular value decomposition provides left and right singular vectors, and the eigenvalue decomposition provides eigenvectors. The transmitting station uses the right singular vectors or the eigenvectors to transmit data on the S eigenmodes. The receiving station uses the left singular vectors or the eigenvectors to receive data transmitted on the S eigenmodes.
Eigenvalue decomposition and singular value decomposition are very computationally intensive. There is therefore a need in the art for techniques to efficiently decompose matrices.